Applets to Enrich Teaching Probability and Statistics

We present didactically-inspired dynamic visualisations, which we use in our introductory

courses (for mathematics students and students of other studies) in order to support

comprehending the more complex concepts. Our principles in designing the applets are signified

by the following ideas:

* An abstract concept of probability may be illustrated by its traces in relative frequencies in

repeated experiments.

* The meaning of parameters of probability models may be enhanced by showing the effect of

systematic changes of these parameters.

* Central theorems (limiting theorems) are enhanced by simulation; however, rather than

“showing” a limiting behavior, which cannot be represented materially, we focus on

establishing a stable pattern, which inspires a thought experiment that finally enhances the

theorem.

All the applets share the exploration of a dynamic change of the initial situation. Like in a

video, one looks at the different stages of emergence of a relation between the investigated

concepts.